Hyperbolic discounting is more complex to model and problematic in terms of overcoming cognitive biases, however, the framework raises an important question concerning whether decreasing discount rates over time are more appropriate for longer-term investments, specifically, environmental and social investments where long-term value creation far surpasses traditional investment horizons. The growth of global investment in climate mitigation, adaptation, and alternatives to fossil fuels can be seen as the direct consequence of global warming are becoming more severe. 55 In this context, investment decision-making models that reflect this trend may offer an enhanced investment perspective. This builds on addressing the limitation we outlined above, in terms of exponentially discounted value vs. compounding value over time. Table 1 below sets out the key distinctions between exponential and hyperbolic discounting.
Aspect
Exponential discounting
Hyperbolic discounting
Discount rate behaviour
Constant over time; the rate at which future rewards are discounted remains unchanged regardless of the time delay. Time-consistent; preferences between two future moments remain consistent over time.
Decreases over time; immediate rewards are more heavily discounted, but as the delay increases, the discount
rate diminishes, leading to less discounting of future rewards.
Time consistency
Time-inconsistent; preferences can change over time, leading to dynamic inconsistencies such as preference reversals. The value of a future reward decreases more rapidly in the short-term and
Mathematical representation
The value of a future reward decreases exponentially as time goes by.
more slowly in the longer-term following a hyperbolic curve.
Behavioural implications
Assumes unbounded rationality-based decision-making with consistent preferences over time.
Assumes bounded rationality decision- making for observed human behaviours like present bias, where individuals disproportionately prefer immediate rewards over future ones. An individual faced with same choice now, or $150 in one year or $160 in 18 months may demonstrate different choices illustrating changing preferences over time.
Example
An individual’s relative preference of $100 today, vs. $110 in the future, remains constant assuming a fixed discount rate.
Table 1: Comparison Between Exponential and Hyperbolic Discounting.
Beyond behavioural formulations such as hyperbolic discounting, several alternative models have been advanced to represent uncertainty in future discount rates. Stochastic discounting frameworks treat the rate itself as a variable that evolves with macroeconomic or policy uncertainty (Weitzman, 2001; Gollier, 2002), while gamma discounting integrates across a probability distribution of exponential rates to yield an empirically declining effective rate over time (Weitzman, 2010). Both approaches reinforce the rationale for time-varying discount rates, linking their decline to uncertainty in long-term economic conditions rather than solely to preference dynamics, thereby complementing the behavioural perspective outlined above.
55 See: Dasgupta, A. (2025). Climate Finance Is a Top Story to Watch in 2025. World Resources Institute. Available at: https://www.wri.org/insights/climate-finance-progress-2025.
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